1. Molecular Geometry and Bonding Theories
David P. White
University of North Carolina, Wilmington
Chapter 9
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2. Molecular Shapes
Lewis structures give atomic connectivity: they tell us which atoms are physically connected to which.
The shape of a molecule is determined by its bond angles.
Consider CCl4: experimentally we find all Cl-C-Cl bond angles are 109.5.
Therefore, the molecule cannot be planar.
All Cl atoms are located at the vertices of a tetrahedron with the C at its center.
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3. Molecular Shapes
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4. Molecular Shapes
In order to predict molecular shape, we assume the valence electrons repel each other. Therefore, the molecule adopts whichever 3D geometry minimized this repulsion.
We call this process Valence Shell Electron Pair Repulsion (VSEPR) theory.
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5. The VSEPR Model
The valence electrons in a molecule are the bonding pairs of electrons as well as the lone pairs.
There are 11 shapes that are important to us:
linear (3 atoms, AB2); bent (3 atoms, AB2);
trigonal planar (4 atoms, AB3); trigonal pyramidal (4 atoms, AB3); T-shaped (4 atoms, AB3);
tetrahedral (5 atoms, AB4); square planar (5 atoms, AB4); see-saw (5 atoms, AB4);
trigonal bipyramidal (6 atoms, AB5); square pyramidal (6 atoms, AB5); and
octahedral (7 atoms, AB6).
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6. The VSEPR Model
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7. The VSEPR Model Predicting Molecular Geometries
To determine the shape of a molecule, we distinguish between lone pairs (or non-bonding pairs, those not in a bond) of electrons and bonding pairs (those found between two atoms).
We define the electron pair geometry by the positions in 3D space of ALL electron pairs (bonding or non-bonding).
The electrons adopt an arrangement in space to minimize e--e- repulsion.
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8. The VSEPR Model Predicting Molecular Geometries
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9. The VSEPR Model Predicting Molecular Geometries
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10. The VSEPR Model Predicting Molecular Geometries
To determine the electron pair geometry:
draw the Lewis structure
count the total number of electron pairs around the central atom
arrange the electron pairs in one of the above geometries to minimize e--e- repulsion
multiple bounds count as one bonding pair
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11. The VSEPR Model Predicting Molecular Geometries
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12. The VSEPR Model Predicting Molecular Geometries
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13. The VSEPR Model
The Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles
We determine the electron pair geometry only looking at electrons.
We name the molecular geometry by the positions of atoms.
We ignore lone pairs in the molecular geometry.
All the atoms that obey the octet rule have tetrahedral electron pair geometries.
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14. The VSEPR Model
The Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles
By experiment, the H-X-H bond angle decreases on moving from C to N to O:
Since electrons in a bond are attracted by two nuclei, they do not repel as much as lone pairs.
Therefore, the bond angle decreases as the number of lone pairs increase.
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15. The VSEPR Model
The Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles
Similarly, electrons in multiple bonds repel more than electrons in single bonds.
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16. The VSEPR Model Molecules with Expanded Valence Shells
Atoms that have expanded octets have AB5 (trigonal bipyramidal) or AB6 (octahedral) electron pair geometries.
For trigonal bipyramidal structures there is a plane containing three electrons pairs. The fourth and fifth electron pairs are located above and below this plane.
For octahedral structures, there is a plane containing four electron pairs. Similarly, the fifth and sixth electron pairs are located above and below this plane.
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17. The VSEPR Model Molecules with Expanded Valence Shells
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18. The VSEPR Model Molecules with Expanded Valence Shells
To minimize e--e- repulsion, lone pairs are always placed in equatorial positions.
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19. The VSEPR Model Molecules with Expanded Valence Shells
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20. The VSEPR Model Molecules with More than One Central Atom
In acetic acid, CH3COOH, there are three central atoms.
We assign the geometry about each central atom separately.
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21. Polarity of Molecules Polar molecules interact with electric fields.
If the centers of negative and positive charge do not coincide, then the molecule is polar.
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22. Polarity of Molecules Dipole Moments of Polyatomic Molecules
If two charges, equal in magnitude and opposite in sign, are separated by a distance r, then a dipole is established.
The dipole moment, m, is given by
m = Qr
where Q is the magnitude of charge.
Dipole Moments of Polyatomic Molecules
In a polyatomic molecule, each bond can be a dipole.
The orientation of these individual dipole moments determines whether the molecule has an overall dipole moment.
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23. Polarity of Molecules Dipole Moments of Polyatomic Molecules
Example: in CO2, each C-O dipole is canceled because the molecule is linear. In H2O, the H-O dipoles do not cancel because the molecule is bent.
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24. Polarity of Molecules Dipole Moments of Polyatomic Molecules
It is possible for a molecule with polar bonds to be either polar or non-polar.
For diatomic molecules:
polar bonds always result in an overall dipole moment.
For triatomic molecules:
if the molecular geometry is trigonal pyramidal, there is an overall dipole moment;
if the molecular geometry is trigonal planar and all three bonds are identical, there is no overall dipole moment;
if the molecular geometry is trigonal planar and one or two bonds are different, there is an overall dipole moment.
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25. Polarity of Molecules Dipole Moments of Polyatomic Molecules
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26. Polarity of Molecules Dipole Moments of Polyatomic Molecules
For tetraatomic molecules with identical bonds:
if the molecular geometry is tetrahedral or square planar, then the molecules are nonpolar;
if the molecular geometry is see-saw, the molecule is polar.
For tetraatomic molecules in which one, two, or three bonds are different:
the molecule is polar.
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27. Covalent Bonding and Orbital Overlap
Lewis structures and VSEPR do not explain why a bond forms.
How do we account for shape in terms of quantum mechanics?
What are the orbitals that are involved in bonding?
We use Valence Bond Theory:
Bonds form when orbitals on atoms overlap.
There are two electrons of opposite spin in the orbital overlap.
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28. Covalent Bonding and Orbital Overlap
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29. Covalent Bonding and Orbital Overlap
As two nuclei approach each other their atomic orbitals overlap.
As the amount of overlap increases, the energy of the interaction decreases.
At some distance the minimum energy is reached.
The minimum energy corresponds to the bonding distance (or bond length).
As the two atoms get closer, their nuclei begin to repel and the energy increases.
At the bonding distance, the attractive forces between nuclei and electrons just balance the repulsive forces (nucleus-nucleus, electron-electron).
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30. Covalent Bonding and Orbital Overlap
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31. Hybrid Orbitals sp Hybrid Orbitals
Consider the BeF2 molecule (experimentally known to exist):
Be has a 1s22s2 electron configuration.
There is no unpaired electron available for bonding.
We conclude that the atomic orbitals are not adequate to describe orbitals in molecules.
We know that the F-Be-F bond angle is 180 (VSEPR theory).
We also know that one electron from Be is shared with each one of the unpaired electrons from F.
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32. Hybrid Orbitals sp Hybrid Orbitals
We assume that the Be orbitals in the BeF bond are 180 apart.
We could promote and electron from the 2s orbital on Be to the 2p orbital to get two unpaired electrons for bonding.
BUT the geometry is still not explained.
We can solve the problem by allowing the 2s and one 2p orbital on Be to mix or form a hybrid orbital (process called hybridization).
The hybrid orbital comes from an s and a p orbital and is called an sp hybrid orbital.
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33. Hybrid Orbitals sp Hybrid Orbitals
The two lobes of an sp hybrid orbital are 180 apart.
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34. Hybrid Orbitals sp Hybrid Orbitals
Since only one of the Be 2p orbitals has been used in hybridization, there are two unhybridized p orbitals remaining on Be.
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35. Hybrid Orbitals sp2 and sp3 Hybrid Orbitals
Important: when we mix n atomic orbitals we must get n hybrid orbitals.
sp2 hybrid orbitals are formed with one s and two p orbitals. (Therefore, there is one unhybridized p orbital remaining.)
The large lobes of sp2 hybrids lie in a trigonal plane.
All molecules with trigonal planar electron pair geometries have sp2 orbitals on the central atom.
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36. Hybrid Orbitals sp2 and sp3 Hybrid Orbitals
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37. Hybrid Orbitals sp2 and sp3 Hybrid Orbitals
sp3 Hybrid orbitals are formed from one s and three p orbitals. Therefore, there are four large lobes.
Each lobe points towards the vertex of a tetrahedron.
The angle between the large lobs is 109.5
All molecules with tetrahedral electron pair geometries are sp3 hybridized.
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38. Hybrid Orbitals sp2 and sp3 Hybrid Orbitals
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39. Hybrid Orbitals Hybridization Involving d Orbitals
Since there are only three p-orbitals, trigonal bipyramidal and octahedral electron pair geometries must involve d-orbitals.
Trigonal bipyramidal electron pair geometries require sp3d hybridization.
Octahedral electron pair geometries require sp3d2 hybridization.
Note the electron pair geometry from VSEPR theory determines the hybridization.
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40. Hybrid Orbitals
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41. Hybrid Orbitals
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42. Hybrid Orbitals Summary To assign hybridization:
draw a Lewis structure;
assign the electron pair geometry using VSEPR theory;
from the electron pair geometry, determine the hybridization; and
name the geometry by the positions of the atoms.
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43. Multiple Bonds
-Bonds: electron density lies on the axis between the nuclei.
All single bonds are -bonds.
-Bonds: electron density lies above and below the plane of the nuclei.
A double bond consists of one -bond and one -bond.
A triple bond has one -bond and two -bonds.
Often, the p-orbitals involved in -bonding come from unhybridized orbitals.
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44. Multiple Bonds
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45. Multiple Bonds Ethylene, C2H4, has: one - and one -bond;
both C atoms sp2 hybridized;
both C atoms with trigonal planar electron pair and molecular geometries.
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46. Multiple Bonds Consider acetylene, C2H2
the electron pair geometry of each C is linear;
therefore, the C atoms are sp hybridized;
the sp hybrid orbitals form the C-C and C-H -bonds;
there are two unhybridized p-orbitals;
both unhybridized p-orbitals form the two -bonds;
one -bond is above and below the plane of the nuclei;
one -bond is in front and behind the plane of the nuclei.
When triple bonds form (e.g. N2) one -bond is always above and below and the other is in front and behind the plane of the nuclei.
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47. Multiple Bonds Delocalized p Bonding
So far all the bonds we have encountered are localized between two nuclei.
In the case of benzene
there are 6 C-C  bonds, 6 C-H  bonds,
each C atom is sp2 hybridized,
and there are 6 unhybridized p orbitals on each C atom.
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48. Multiple Bonds Delocalized p Bonding Copyright 1999, PRENTICE HALL
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49. Multiple Bonds Delocalized p Bonding
In benzene there are two options for the 3  bonds
localized between C atoms or
delocalized over the entire ring (i.e. the  electrons are shared by all 6 C atoms).
Experimentally, all C-C bonds are the same length in benzene.
Therefore, all C-C bonds are of the same type (recall single bonds are longer than double bonds).
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50. Multiple Bonds Delocalized p Bonding Copyright 1999, PRENTICE HALL
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51. Multiple Bonds General Conclusions
Every two atoms share at least 2 electrons.
Two electrons between atoms on the same axis as the nuclei are  bonds.
-Bonds are always localized.
If two atoms share more than one pair of electrons, the second and third pair form -bonds.
When resonance structures are possible, delocalization is also possible.
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52. Molecular Orbitals
Some aspects of bonding are not explained by Lewis structures, VSEPR theory and hybridization. (E.g. why does O2 interact with a magnetic field?; Why are some molecules colored?)
For these molecules, we use Molecular Orbital (MO) Theory.
Just as electrons in atoms are found in atomic orbitals, electrons in molecules are found in molecular orbitals.
Molecular orbitals:
each contain a maximum of two electrons;
have definite energies;
can be visualized with contour diagrams;
are associated with an entire molecule.
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53. Molecular Orbitals The Hydrogen Molecule
When two AOs overlap, two MOs form.
Therefore, 1s (H) + 1s (H) must result in two MOs for H2:
one has electron density between nuclei (bonding MO);
one has little electron density between nuclei (antibonding MO).
MOs resulting from s orbitals are  MOs.
 (bonding) MO is lower energy than * (antibonding) MO.
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54. Molecular Orbitals The Hydrogen Molecule Copyright 1999, PRENTICE HALL
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55. Molecular Orbitals The Hydrogen Molecule
Energy level diagram or MO diagram shows the energies and orbitals in an orbital.
The total number of electrons in all atoms are placed in the MOs starting from lowest energy (1s) and ending when you run out of electrons.
Note that electrons in MOs have opposite spins.
H2 has two bonding electrons.
He2 has two bonding electrons and two antibonding electrons.
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56. Molecular Orbitals The Hydrogen Molecule Copyright 1999, PRENTICE HALL
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57. Molecular Orbitals Bond Order
Define Bond Order = ½(bonding electrons - antibonding electrons).
Bond order = 1 for single bond.
Bond order = 2 for double bond.
Bond order = 3 for triple bond.
Fractional bond orders are possible.
Bond order for H2 = ½(bonding electrons - antibonding electrons) = ½(2 -0) = 1.
Therefore, H2 has a single bond.
Bond order for He2 = ½(bonding electrons - antibonding electrons) = ½(2 - 2) = 0.
Therefore He2 is not a stable molecule.
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58. Second-Row Diatomic Molecules
We look at homonuclear diatomic molecules (e.g. Li2, Be2, B2 etc.).
AOs combine according to the following rules:
The number of MOs = number of AOs;
AOs of similar energy combine (e.g. 1s + 1s rather than 1s + 2s);
As overlap increases, the energy of the MO decreases;
Pauli: each MO has at most two electrons;
Hund: for degenerate orbitals, each MO is first occupied singly.
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59. Second-Row Diatomic Molecules
Molecular Orbitals for Li2 and Be2
Each 1s orbital combines with another 1s orbital to give one 1s and one *1s orbital, both of which are occupied (since Li and Be have 1s2 electron configurations).
Each 2s orbital combines with another 2s orbital, two give one 2s and one *2s orbital.
The energies of the 1s and 2s orbitals are sufficiently different so that there is no cross-mixing of orbitals (i.e. we do not get 1s + 2s).
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60. Second-Row Diatomic Molecules
Molecular Orbitals for Li2 and Be2
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61. Second-Row Diatomic Molecules
Molecular Orbitals for Li2 and Be2
There are a total of 6 electrons in Li2:
2 electrons in 1s;
2 electrons in *1s;
2 electrons in 2s; and
0 electrons in *2s.
Therefore the bond order is ½(4 - 2) = 1.
Since the 1s AOs are completely filled, the 1s and *1s are filled. We generally ignore core electrons in MO diagrams.
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62. Second-Row Diatomic Molecules
Molecular Orbitals for Li2 and Be2
There are a total of 8 electrons in Be2:
2 electrons in 1s;
2 electrons in *1s;
2 electrons in 2s; and
2 electrons in *2s.
Therefore, the bond order is ½(4 - 4) = 0.
Be2 does not exist.
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63. Second-Row Diatomic Molecules
Molecular Orbitals from 2p Atomic Orbitals
There are two ways in which two p orbitals overlap:
end-on so that the resulting MO has electron density on the axis between nuclei (i.e.  type orbital);
sideways so that the resulting MO has electron density above and below the axis between nuclei (i.e.  type orbital).
The six p-orbitals (two sets of 3) must give rise to 6 MOs:
, *, , *, , and *.
Therefore there is a maximum of 2  bonds that can come from p-orbitals.
The relative energies of these six orbitals can change.
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64. Second-Row Diatomic Molecules
Molecular Orbitals from 2p Atomic Orbitals
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65. Second-Row Diatomic Molecules
Electron Configurations for B2 through Ne2
2s Orbitals are lower in energy than 2p orbitals so 2s orbitals are lower in energy than 2p orbitals.
There is greater overlap between 2pz orbitals (they point directly towards one another) so the 2p is MO is lower in energy than the 2p orbitals.
There is greater overlap between 2pz orbitals so the *2p is MO is higher in energy than the *2p orbitals.
The 2p and *2p orbitals are doubly degenerate.
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66. Second-Row Diatomic Molecules
Electron Configurations for B2 through Ne2
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67. Second-Row Diatomic Molecules
Electron Configurations for B2 through Ne2
As the atomic number decreases, it becomes more likely that a 2s orbital on one atom can interact with the 2p orbital on the other.
As the 2s-2p interaction increases, the 2s MO lowers in energy and the 2p orbital increases in energy.
For B2, C2 and N2 the 2p orbital is higher in energy than the 2p.
For O2, F2 and Ne2 the 2p orbital is higher in energy than the 2p.
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68. Second-Row Diatomic Molecules
Electron Configurations for B2 through Ne2
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69. Second-Row Diatomic Molecules
Electron Configurations for B2 through Ne2
Once the relative orbital energies are known, we add the required number of electrons to the MOs, taking into account Pauli’s exclusion principle and Hund’s rule.
As bond order increases, bond length decreases.
As bond order increases, bond energy increases.
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70. Second-Row Diatomic Molecules
Electron Configurations for B2 through Ne2
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71. Second-Row Diatomic Molecules
Electron Configurations and Molecular Properties
Two types of magnetic behavior:
paramagnetism (unpaired electrons in molecule): strong attraction between magnetic field and molecule;
diamagnetism (no unpaired electrons in molecule): weak repulsion between magnetic field and molecule.
Magnetic behavior is detected by determining the mass of a sample in the presence and absence of magnetic field:
large increase in mass indicates paramagnetism,
small decrease in mass indicates diamagnetism.
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72. Second-Row Diatomic Molecules
Electron Configurations and Molecular Properties
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73. Second-Row Diatomic Molecules
Electron Configurations and Molecular Properties
Experimentally O2 is paramagnetic.
The Lewis structure for O2 shows no unpaired electrons.
The MO diagram for O2 shows 2 unpaired electrons in the *2p orbital.
Experimentally, O2 has a short bond length (1.21 Å) and high bond dissociation energy (495 kJ/mol). This suggests a double bond.
The MO diagram for O2 predicts both paramagnetism and the double bond (bond order = 2).
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74. Second-Row Diatomic Molecules
Electron Configurations and Molecular Properties
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75. Molecular Geometry and Bonding Theories
End of Chapter 9
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